I installed A1 Visual Tasks as trial, never really used it so I forgot about it and decided to check it out now. It says "Trial Mode: -1 days left" but I can still use it fully. What are the "rules" when it comes to trial version of paid apps?

If it's a time limited trial, once the time limit expires, you will be unable to launch it again the next time it's closed (whether you manually kill it, reboot, or the system terminates it to free up memory). Before that happens, it's up to the app author to detect that the license has expired and close the app, do something like put up a barricade page, or do nothing and wait until the next close/reboot/etc to enforce the expiration.